Question 1

Solve the problem.
-In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at $0.314$ arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about $150,000,000 \mathrm {~km}$ and $\theta = 0.314$ seconds $= \frac { 0.314 } { 60 }$ minutes $= \frac { 0.314 } { 60 \cdot 60 }$ degrees, determine the distance d from Earth to 61 Cygni using Bessel's figures. Express the answer in scientific notation.

Accepted Answer

A)  $1.97 \times 10 ^ { 14 } \mathrm {~km}$ 
B)  $1.05 \times 10 ^ { 14 } \mathrm {~km}$ 
C)  $2.28 \times 10 ^ { 13 } \mathrm {~km}$ 
D)  $9.85 \times 10 ^ { 13 } \mathrm {~km}$

Question 2

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
-Find $\cos \mathrm { A }$ when $\mathrm { a } = \sqrt { 7 }$ and $\mathrm { c } = 6$.

Accepted Answer

A)  $\frac { 7 } { 6 }$ 
B)  $\frac { 29 } { 7 }$ 
C)  $\frac { \sqrt { 29 } } { 6 }$ 
D)  $\frac { \sqrt { 7 } } { 6 }$

Question 3

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-cot ϴ = 1.7009187

Accepted Answer

A) 59.5479812° 
B) 36.0093720° 
C) 30.4520188° 
D) 53.9906280°

Question 4

Find the reference angle for the given angle.
--7.5°

Accepted Answer

A) 83° 
B) 82.5° 
C) 8° 
D) 7.5°

Question 5

Decide whether the statement is true or false.
-sin 86° > sin 24°

Accepted Answer

A) True 
 B)False

Question 6

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using
the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize
the denominator if applicable.
-Find $\sin \mathrm { A }$ when $\mathrm { a } = 4$ and $\mathrm { b } = 5$.

Accepted Answer

A)  $\frac { \sqrt { 41 } } { 4 }$ 
B)  $\frac { 4 \sqrt { 41 } } { 41 }$ 
C)  $\frac { \sqrt { 41 } } { 5 }$ 
D)  $\frac { 5 \sqrt { 41 } } { 41 }$

Question 7

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-cos 31.2°

Accepted Answer

A) cos 148.8° 
B) sin 58.8° 
C) sec 148.8° 
D) sin 31.2°

Question 8

Solve the problem.
-A conservation officer needs to know the width of a river in order to set instruments correctly for a study of pollutants in the river. From point A, the conservation officer walks 100 feet downstream
And sights point B on the opposite bank to determine that ϴ = 30° (see figure). How wide is the river
(round to the nearest foot)?

Accepted Answer

A)  $115 \mathrm { ft }$ 
B)  $173 \mathrm { ft }$ 
C)  $50 \mathrm { ft }$ 
D)  $58 \mathrm { ft }$

Question 9

Find the exact value of the expression.
-sin (-2040°)

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $- 1$

Question 10

Find the exact value of the expression.
-$\cot \left( - 1575 ^ { \circ } \right)$

Accepted Answer

A)  $- 1$ 
B)  $\frac { \sqrt { 3 } } { 3 }$ 
C)  $\sqrt { 3 }$ 
D)  1

Question 11

Solve the problem.
-A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed, the angle of depression to the car is 45° 56´. When the car
Stops, the angle of depression is 22° 34´. The building is 270 feet tall. How far did the car travel from
When it was first noticed until it stopped? Round to the nearest foot.

Accepted Answer

A) 415 ft 
B) 588 ft 
C) 367 ft 
D) 388 ft

Question 12

Solve the problem.
-The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin ϴ where W is the weight of the car and ϴ is the angle of the hill's grade (ϴ > 0 for uphill travel, ϴ < 0
For downhill travel). What is the grade resistance (to the nearest pound)of a 3000-lb car traveling
Uphill on a 3° grade (ϴ = 3°)?

Accepted Answer

A) 157 lb 
B) -3003 lb 
C) -157 lb 
D) 3003 lb

Question 13

Find all values of , if is in the interval [0, 360°) and has the given function value.
-$\sec \theta$ is undefined

Accepted Answer

A)  $0 ^ { \circ }$ 
B)  $0 ^ { \circ }$ and $180 ^ { \circ }$ 
C)  $90 ^ { \circ }$ 
D)  $90 ^ { \circ }$ and $270 ^ { \circ }$

Question 14

Find the exact value of the expression.
-$\tan 300 ^ { \circ }$

Accepted Answer

A)  $- \sqrt { 3 }$ 
B)  $\frac { \sqrt { 3 } } { 3 }$ 
C)  $\sqrt { 3 }$ 
D)  $- \frac { \sqrt { 3 } } { 3 }$

Question 15

Solve the problem for the given information.
-Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$-axis is $\frac { 1 } { 2 }$.

Accepted Answer

A)  $y = \frac { \sqrt { 3 } } { 3 } x$ 
B)  $y = \frac { 1 } { 2 } x$ 
C)  $y = \sqrt { 3 } x$ 
D)  $y = \frac { \sqrt { 3 } } { 2 } x$

Question 16

Decide whether the statement is true or false.
-$$\cos 43 ^ { \circ } \leq \cos 5 ^ { \circ }$$

Accepted Answer

A) True 
 B)False

Question 17

Determine whether the statement is true or false.
-sin 120° = 2 sin 60° cos 60°

Accepted Answer

A) True 
 B)False

Question 18

Find the exact value of the expression.
-sin 2835°

Accepted Answer

A)  $2 \sqrt { 3 }$ 
B)  $- \frac { \sqrt { 3 } } { 2 }$ 
C)  $- \frac { \sqrt { 2 } } { 2 }$ 
D)  $- \frac { 1 } { 2 }$

Question 19

Solve the problem.
-The length of the base of an isosceles triangle is 33.28 meters. Each base angle is 37.57°. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.

Accepted Answer

A) 27.29 m 
B) 21.63 m 
C) 41.99 m 
D) 20.99 m

Question 20

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-sec ϴ = 2.7259498

Accepted Answer

A) 21.5211475° 
B) 68.4788525° 
C) 54.5922708° 
D) 20.1452902°

Exam 2: Acute Angles and Right Triangles

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -cot ϴ = 1.7009187

Find the reference angle for the given angle. --7.5°

Decide whether the statement is true or false. -sin 86° > sin 24°

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -cos 31.2°

Find the exact value of the expression. -sin (-2040°)

Find the exact value of the expression. - $\cot \left( - 1575 ^ { \circ } \right)$

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\sec \theta$ is undefined

Find the exact value of the expression. - $\tan 300 ^ { \circ }$

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { 1 } { 2 }$ .

Decide whether the statement is true or false. - $\cos 43 ^ { \circ } \leq \cos 5 ^ { \circ }$

Determine whether the statement is true or false. -sin 120° = 2 sin 60° cos 60°

Find the exact value of the expression. -sin 2835°

Solve the problem. -The length of the base of an isosceles triangle is 33.28 meters. Each base angle is 37.57°. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -sec ϴ = 2.7259498

Exam 2: Acute Angles and Right Triangles

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -cot ϴ = 1.7009187

Find the reference angle for the given angle. --7.5°

Decide whether the statement is true or false. -sin 86° > sin 24°

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. -cos 31.2°

Find the exact value of the expression. -sin (-2040°)

Find the exact value of the expression. - cot⁡(−1575∘) \cot \left( - 1575 ^ { \circ } \right) cot(−1575∘)

Find all values of , if is in the interval [0, 360°) and has the given function value. - sec⁡θ\sec \thetasecθ is undefined

Find the exact value of the expression. - tan⁡300∘\tan 300 ^ { \circ }tan300∘

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant III and the positive xxx -axis is 12\frac { 1 } { 2 }21​ .

Decide whether the statement is true or false. - cos⁡43∘≤cos⁡5∘\cos 43 ^ { \circ } \leq \cos 5 ^ { \circ }cos43∘≤cos5∘

Determine whether the statement is true or false. -sin 120° = 2 sin 60° cos 60°

Find the exact value of the expression. -sin 2835°

Solve the problem. -The length of the base of an isosceles triangle is 33.28 meters. Each base angle is 37.57°. Find the length of each of the two equal sides of the triangle. Round your answer to the hundredths place.

Find a value of in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -sec ϴ = 2.7259498

Find the exact value of the expression. - $\cot \left( - 1575 ^ { \circ } \right)$

Find all values of , if is in the interval [0, 360°) and has the given function value. - $\sec \theta$ is undefined

Find the exact value of the expression. - $\tan 300 ^ { \circ }$

Solve the problem for the given information. -Find the equation of a line passing through the origin so that the cosine of the angle between the line in quadrant $I$ and the positive $x$ -axis is $\frac { 1 } { 2 }$ .

Decide whether the statement is true or false. - $\cos 43 ^ { \circ } \leq \cos 5 ^ { \circ }$